Finite Group Databasebeta

← C23×#1616 #15669235

Subgroups — C23×#1616 #15669235

Order 2944.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#537C211yesmaximal, characteristic
2C23×#481C212yesmaximal, complemented
3C23×#400C211yesmaximal, characteristic, complemented
4C23×#327C212yesmaximal, complemented
5C23×#324C211yesmaximal, characteristic, complemented
6C2×#41×C23—21no—
7C23×C22⋊Q8—22no—
8C23×#121—22no—
9C23×#121—21no—
10C23×#121C2212yes—
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C23×#106—22no—
14C23×#102—22no—
15C23×C22⋊C8C2212yes—
16C23×#95—21no—
17C23×#95—21no—
18C23×#95C2211yescharacteristic
19#41×C23—42no—
20#41×C23—42no—
21C2×Q8×C23—21no—
22C2×D4×C23—21no—
23C2×D4×C23—22no—
24C2×D4×C23—21no—
25C2×D4×C23D412yes—
26C22×C4×C23—22no—
27C22×C4×C23—21no—
28C22×C4×C23—21no—
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C2×C8×C23—22no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—22no—
35C4⋊C4×C23—22no—
36C4⋊C4×C23D412yes—
37C22⋊C4×C23—22no—
38C22⋊C4×C23—22no—
39C23×C23—22no—
40C23×C23C2×D411yescharacteristic
41Q8×C23—42no—
42D4×C23—42no—
43D4×C23—42no—
44D4×C23—42no—
45D4×C23—42no—
46D4×C23—81no—
47C2×C4×C23—21no—
48C2×C4×C23—21no—
49C2×C4×C23—21no—
50C2×C4×C23—22no—
51C2×C4×C23—41no—
52C2×C4×C23—44no—
53C2×C4×C23—41no—
54C2×C4×C23—41no—
55C2×C4×C23—41no—
56C2×C4×C23—42no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23SD1612yes—
60C2×C4×C23C2×D412yes—
61C8×C23—42no—
62#1616C2311yesmaximal, characteristic, direct product factor, Sylow
63C22×C23—21no—
64C22×C23—21no—
65C22×C23—42no—
66C22×C23—42no—
67C22×C23—42no—
68C22×C23#12011yescharacteristic
69C22×C23C2×SD1611yescharacteristic
70C22×C23AGL(1,ℤ/8)11yescharacteristic
71C4×C23—22no—
72C4×C23—22no—
73C4×C23—42no—
74C4×C23—41no—
75C4×C23—81no—
76C4×C23—81no—
77#537C2×C2311yescharacteristic
78#481C2×C2312yescomplemented
79#400C2×C2311yescharacteristic, complemented
80#327C2×C2312yescomplemented
81#324C2×C2311yescharacteristic, complemented
82C2×C23—21no—
83C2×C23—21no—
84C2×C23—82no—
85C2×C23#45011yescharacteristic
86C2×C23#45411yescharacteristic
87C2×C23#45811yescharacteristic
88C2×#41—21no—
89C22⋊Q8—22no—
90#121—22no—
91#121—21no—
92#121C22×C2312yes—
93C2×C4⋊C4C22×C2311yescharacteristic
94C2×C4⋊C4C22×C2311yescharacteristic
95#106—22no—
96#102—22no—
97C22⋊C8C22×C2312yes—
98#95—21no—
99#95—21no—
100#95C22×C2311yescharacteristic
101C23#161611yescharacteristic, direct product factor, Sylow
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4D4×C2312yes—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4D4×C2311yescharacteristic
113C22×C4D4×C2311yescharacteristic
114C22×C4C23×C2311yescharacteristic
115C2×C8—22no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—22no—
119C4⋊C4D4×C2312yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×D4×C2311yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4SD16×C2312yes—
143C2×C4C2×D4×C2312yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22C23×#12011yescharacteristic
151C22C2×SD16×C2311yescharacteristic
152C22C23×AGL(1,ℤ/8)11yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—81no—
158C4—81no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2C23×#45011yescharacteristic
163C2C23×#45411yescharacteristic
164C2C23×#45811yescharacteristic
subgroupG/H
center, socleC22×C23#120
commutator, Frattini, cosocleC22×C4C23×C23
prime radicalC23×#537C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C23×#481C2semidirect
3. C23×#400C2semidirect
4. C23×#327C2semidirect
5. C23×#324C2semidirect
62. #1616C23direct (N × H)
78. #481C2×C23semidirect
79. #400C2×C23semidirect
80. #327C2×C23semidirect
81. #324C2×C23semidirect
101. C23#1616direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#5372
C23×#4812
C23×#4002
C23×#3272
C23×#3242
#161623